High order discretization methods for spatial-dependent epidemic models

Bálint Takács and Yiannis Hadjimichael

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 198, issue C, 211-236

Abstract: In this paper, an epidemic model with spatial dependence is studied and results regarding its stability and numerical approximation are presented. We consider a generalization of the original Kermack and McKendrick model in which the size of the populations differs in space. The use of local spatial dependence yields a system of partial-differential equations with integral terms. The uniqueness and qualitative properties of the continuous model are analyzed. Furthermore, different spatial and temporal discretizations are employed, and step-size restrictions for the discrete model’s positivity, monotonicity preservation, and population conservation are investigated. We provide sufficient conditions under which high-order numerical schemes preserve the stability of the computational process and provide sufficiently accurate numerical approximations. Computational experiments verify the convergence and accuracy of the numerical methods.

Keywords: Epidemic models; SIR model; Integro-differential equations; Strong stability preservation (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:198:y:2022:i:c:p:211-236

DOI: 10.1016/j.matcom.2022.02.021

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